Main Content

Centrifugal pump in isothermal liquid network

**Library:**Simscape / Fluids / Isothermal Liquid / Pumps & Motors

The Centrifugal Pump (IL) block represents a centrifugal pump that transfers energy from the shaft to a fluid in an isothermal liquid network. The pressure differential and mechanical torque are functions of the pump head and brake power, which depend on pump capacity. You can parameterize the pump analytically or by linear interpolation of tabulated data. The pump affinity laws define the core physics of the block, which scale the pump performance to the ratio of the current to the reference values of the pump angular velocity and impeller diameter.

By default, the flow and pressure gain are
from port **A** to port **B**. Port
**C** represents the pump casing, and port **R**
represents the pump shaft. You can specify the normal operating shaft direction in the
**Mechanical orientation** parameter. If the shaft begins to spin
in the opposite direction, the pressure difference across the block drops to
zero.

**Port Configuration**

The figure shows the location of the block ports on a typical centrifugal pump.

When you set, **Pump parameterization** to ```
Capacity, head,
and brake power at reference shaft speed
```

, the block calculates the
pressure gain over the pump as a function of the pump affinity laws and the
reference pressure differential:

$${p}_{B}-{p}_{A}=\Delta {H}_{ref}\rho g{\left(\frac{\omega}{{\omega}_{ref}}\right)}^{2}{\left(\frac{D}{{D}_{ref}}\right)}^{2},$$

where:

*g*is the gravitational acceleration.*ΔH*is the reference pump head, which the block derives from a quadratic fit of the pump pressure differential between the values of the**Maximum head at zero capacity**,**Nominal head**, and**Maximum capacity at zero head**parameters.*ω*is the shaft angular velocity,*ω*_{R}–*ω*_{C}.*ω*_{ref}is the value of the**Reference shaft speed**parameter.$$\frac{D}{{D}_{ref}}$$ is the value of the

**Impeller diameter scale factor**parameter. This block does not reflect changes in pump efficiency due to pump size.*ρ*is the network fluid density.

The shaft torque is:

$$\tau ={W}_{brake,ref}\frac{{\omega}^{2}}{{\omega}_{ref}^{3}}{\left(\frac{D}{{D}_{ref}}\right)}^{5}.$$

The reference brake power, *W*_{brake,ref},
is calculated as capacity·head/efficiency. The pump efficiency curve is quadratic with its peak
corresponding to the **Nominal brake power** parameter, and it
falls to zero when capacity is zero or maximum as the
pump
curve figure demonstrates.

The block calculates the reference capacity as:

$${q}_{ref}=\frac{\dot{m}}{\rho}\frac{{\omega}_{ref}}{\omega}{\left(\frac{{D}_{ref}}{D}\right)}^{3}.$$

You can choose to be warned when the block flow rate becomes negative or exceeds
the maximum pump capacity by setting **Check if operating beyond normal pump
operation** to `On`

.

When you set **Pump parameterization** to ```
1D tabulated data -
head and brake power vs. capacity at reference shaft speed
```

, the
pressure gain over the pump functions with the **Reference head
vector** parameter, *ΔH*_{ref},
which is a function of the reference capacity,
*q _{ref}*:

$$\Delta p=\rho g\Delta {H}_{ref}({q}_{ref}){\left(\frac{\omega}{{\omega}_{ref}}\right)}^{2}{\left(\frac{D}{{D}_{ref}}\right)}^{2},$$

where *g* is the gravitational acceleration.

The block bases the shaft torque on the **Reference brake power
vector** parameter, *W*_{ref},
which is a function of the reference capacity:

$$\tau ={W}_{ref}({q}_{ref})\frac{{\omega}^{2}}{{\omega}_{ref}^{3}}\left(\frac{\rho}{{\rho}_{ref}}\right){\left(\frac{D}{{D}_{ref}}\right)}^{5},$$

where *ρ _{ref}* is the

$${q}_{ref}=\frac{\dot{m}}{\rho}\left(\frac{{\omega}_{ref}}{\omega}\right){\left(\frac{{D}_{ref}}{D}\right)}^{3},$$

which the block uses to interpolate the values of the
**Reference capacity vector**, **Reference head
vector**, and **Reference brake power vector**
parameters as a function of *q _{ref}*.

When the simulation is outside of the normal pump operating conditions, the block extrapolates the pump head linearly and brake power to the nearest point.

When you set **Pump parameterization** to ```
2D tabulated data -
head and brake power vs. capacity and shaft speed
```

, the pressure
gain over the pump is a function of the **Head table, H(q,w)**
parameter, *ΔH _{ref}*, which is a function of
the reference capacity,

$$\Delta p=\rho g\Delta {H}_{ref}({q}_{ref},\omega ){\left(\frac{D}{{D}_{ref}}\right)}^{2}.$$

The shaft torque is a function of the **Brake power
table, Wb(q,w)** parameter,
*W _{ref}*, which is a function of the
reference capacity,

$$\tau =\frac{{W}_{ref}({q}_{ref},\omega )}{\omega}\left(\frac{\rho}{{\rho}_{ref}}\right){\left(\frac{D}{{D}_{ref}}\right)}^{5}.$$

The reference capacity is:

$${q}_{ref}=\frac{\dot{m}}{\rho}{\left(\frac{{D}_{ref}}{D}\right)}^{3}.$$

When the simulation is outside of the normal pump operating conditions, the block extrapolates the pump head linearly and brake power to the nearest point.

You can check the parameterized pump performance by plotting the head, power,
efficiency, and torque as a function of the flow. To generate a plot of the current
pump settings, right-click on the block and select **Fluids** > **Plot Pump Characteristics**. If you change settings or data, click **Apply** on
the block parameters and click **Reload Data** on the pump curve
figure.

The default block parameterization results in these plots:

You can model a specific supplier component by pre-parameterizing the Centrifugal Pump (IL) block with manufacturer data.

To load a predefined parameterization:

Double-click the block. Click the

**Select a predefined parameterization**hyperlink in the Centrifugal Pump (IL) block dialog description.Select a part from the

**Select manufacturer**and**Select part**drop-down menus, then click**Update block with selected part**.You can compare your current settings with a specific component by clicking

**Compare block settings with selected part**. The differences between the current settings and the pre-defined parameterization display in the MATLAB Command Window.

Reverse flow or a pressure drop over the pump is not normal operation, and the simulation results in these situations may not be accurate.

The block does not account for dynamic pressure in the pump. The block only considers pump head due to static pressure.

Pre-defined parameterizations use available data and the block fills in missing data where necessary. Validate your model against expected results.

Centrifugal Pump (TL) | Variable-Displacement Pump (IL) | Pressure-Compensated Pump (IL) | Fixed-Displacement Pump (IL)